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Squared Bessel processes of positive and negative dimension embedded in Brownian local times

Abstract:

The Ray--Knight theorems show that the local time processes of various path fragments derived from a one-dimensional Brownian motion $B$ are squared Bessel processes of dimensions $0$, $2$, and $4$. It is also known that for various singular perturbations $X= |B| + \mu \ell$ of a reflecting Brownian motion $|B|$ by a multiple $\mu$ of its local time process $\ell$ at $0$, corresponding local time processes of $X$ are squared Bessel with other real dimension parameters, both positive and negat...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.1214/18-ECP174

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More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Statistics
Oxford college:
Brasenose College
Role:
Author
ORCID:
0000-0003-0593-8682
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Electronic Communications in Probability Journal website
Volume:
23
Issue:
2018
Pages:
Article: 74
Publication date:
2018-10-17
Acceptance date:
2018-10-01
DOI:
EISSN:
1083-589X
Pubs id:
pubs:905410
URN:
uri:8930512c-85e3-4e0e-95a3-cab318ea721d
UUID:
uuid:8930512c-85e3-4e0e-95a3-cab318ea721d
Local pid:
pubs:905410

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